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Simplified 2D Transient Heat Transfer Simulation Using Gauss Error Function and FDM

100%

du Plessis M.

Archives of Foundry Engineering

2013

tom Vol. 13, iss. 3 spec.

21--24

This article documents the methodology used to compile a transient heat transfer simulation with the goal of calculating the time to full solidification or any specified temperature of a metal casting, this simulation may serves as a confirmation of Chvorinov's rule, furthermore the simulation will identify the heat transfer topography, allowing the user to identify the location of possible solidification errors, however for the purpose of simplification, only the liquid phase cooling of pure iron will be considered in this report. Euler methods will be discussed with special attention paid to explicit forward approximation and how Gaussian error can be used to simplify the simulation, in an attempt to reduce processing time. A look at the advantages and disadvantages of using this method will be considered and explanations given the decisions taken in the methodology of the simulation, the use of software will be discussed. The article will conclude with a look at the other applications for this simulation as well as the limits of this simulation.

Simple discrete SIS criss-cross model of tuberculosis in heterogeneous population of homeless and non-homeless people

100%

Bodzioch M. , Choiński M.

tom Vol. 47, no. 1

103--115

In this paper we propose a discrete criss-cross model of tuberculosis (TB) transmission in a heterogeneous population, which consists of two different subpopulations: homeless and non-homeless people. This criss-cross model is based on the simple continuous SIS model with bilinear transmission function and constant inflow into both subpopulations considered previously by us. We make preliminary stability analysis. We show that to control the spread of the infectious disease in a heterogeneous population it is not enough to consider the dynamics of the disease in each subpopulation separately. This result is consistent with the result for continuous model. We also fit the model to epidemic data from Warmian-Masurian Province of Poland.

Zaproponowany został dyskretny krzyżowy model rozprzestrzeniania się gruźlicy w niejednorodnej populacji składającej się z bezdomnych i niebezdomnych. Model ten oparty jest na prostym modelu typu SIS z dwuliniową funkcją transmisji i stałym napływem w obu populacjach. Przeprowadzona została wstępna analiza stabilności stanów stacjonarnych. Pokazano, że aby kontrolować rozprzestrzenianie się choroby zakaźnej w niejednorodnej populacji nie jest wystarczające rozważanie dynamiki choroby w każdej podpopulacji oddzielnie. Parametry modelu zostały dopasowane do danych z województwa warmińsko-mazurskiego.

Approximation of functions and their conjugates in Lp and uniform metric by Euler means

80%

Volosivets S. S. , Tyuleneva A. A.

tom Vol. 51, nr 1

141--150

For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.